Abstract
Nonlinear pattern formations have been investigated in many fields. In the field of reacting flow, the oscillatory pattern occurring in a liquid shear flow with a diffusive exothermic reaction has been reported. This oscillatory phenomenon is sensitive to change of viscosity and therefore occur easily near the wall because of the large shear stress. So, its quantitative model is needed to predict and control the oscillation in reactors with very small scale. However, the dynamic mechanism among various factors in the oscillatory pattern formations has not been fully understood. In this study, the relationship between oscillatory patterns and parameters i.e., width, viscosity, flow rate, is experimentally investigated in very narrow rectangular pipe flow and the oscillatory phenomenon is visualized using dye. As the results, it is seen that the flow pattern changes in flow direction and the occurring point of the oscillation is unstable caused by nonlinear interactions among many factors. Fractal analysis is introduced to investigate on the complexity of the nonlinear oscillatory mechanism. Fractal dimension is analyzed in both Lagrangian coordinate and Eulerian coordinate to analyze the characteristics of oscillations, especially changes of the patterns and instability of the occurring points. As the results, it is made clear that there are two types of instability, namely steady instability and unsteady instability. Moreover, fractal dimension for time series data is used to discuss on the effect of viscosity, and the oscillatory patterns changing in time and space are microscopically analyzed by using fractal dimension.
